Supporting Information Spray-Coated Halloysite-Epoxy Composites
Supporting Information Spray-Coated Halloysite-Epoxy Composites: a Means to Create Mechanically Robust, Vertically Aligned Nanotube Composites Kenan Song †, Roberta Polak †, Dayong Chen †, Michael F. Rubner §,* , Khalid A. Askar ◊,* †
‡,*
, Robert E. Cohen
Department of Materials Science and Engineering, Department of Chemical Engineering, and Department of Mechanical Engineering, MIT, 77 Mass Ave, Cambridge, MA, USA, 02139. ‡,* TDK Professor of Polymer Materials Science and Engineering, and Director of CMSE, MIT, 77 Mass Ave, Cambridge, MA, USA, 02139. Correspondence email: [email protected] §,* St. Laurent Professor of Chemical Engineering Department, MIT, 77 Mass Ave, Cambridge, MA, USA, 02139. Correspondence email: [email protected] ◊,* Department of Materials Science and Engineering, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates. Correspondence email: [email protected]
S-1
SI. Viscosity measurements from rheometer
Figure S1. Viscosity vs. shear rate for HNT suspensions in E40A60, E77A23, E87A13, E93A7 and E100A0, showed an increasing viscosity trend with higher epoxy content. The concentration of HNTs in each figure remains constant. The particle concentration only slightly affects the viscosity compared to the significant change caused by the percentage
S-2
of epoxy added. The shear rates in the rheometer measurements are from 10 to 1000 s-1 and the temperature is set at 23 oC. SII. Relaxation time for nanotubes in fluids Shear-aligned halloysite nanotubes were sprayed on a glass slide. The alignment of nanotubes is constrained by the epoxy and given enough time the nanotubes would lose their alignment and reach a state of relaxation. The tilted angle and rate depend on particle features (i.e., length, density, shape), and liquid characteristics (i.e., viscosity, temperature, pressure)1. The fluid consisting of either pure epoxy or different epoxy/acetone mixtures all displayed Newtonian behavior, as shown in Figure S2. The orientation of the body would eventually be determined by inertia1. Bodies with force and front-end symmetry were torque free when settling in Stokes flow, so that the torques due to inertia were unopposed. This resulted in an eventual out-of-plane orientation for all particles1.
Figure S2. Shear stress as a function of shear rates for (a) E100A0 and (b) E93A7 based composites. Linear trends between shear force and shear rate are observed, which exhibits the characteristic of Newtonian fluids. E87A13, E77A23 and E40A60 display the same Newtonian liquid behavior due to the increase in acetone concentration.
S-3
Figure S3. Schematic shows the single halloysite nanotube states of (i) as-ejected into the coating surface, and (ii) reaching steady state, and micromechanics model. Relative flow motion past a falling particle in a fluid (i.e., a halloysite nanotube falling through the epoxy solution or melt) generates drag force, Fd, force due to gravity, Fg, as well as buoyancy, Fb. The sedimentation of the tubes until reaching steady state is equivalent to the steady flow past a stationary long body of halloysite. To simplify the problem, the micromechanics analysis model for a single HNT particle (i.e., diameter of 40 nm and length of 2 µm) falling in a viscous fluid (i.e., viscosity taken from Figure 4) was plotted in Figure S3. The time for the tube to reach steady in-plane state was calculated based on this micromechanics model (Figure S3). According to Stoke’s Law, the force of viscosity on a small particle moving through a viscous fluid is given by2,
Fd = 6πµ Rv
(Equation S1)
where Fd is the friction force, known as Stoke’s drag, acting on the interface between the fluid and particle. µ is the dynamic viscosity. The liquid states studied here are all Newtonian fluids. Viscosity values were taken as a constant from experimental measurements. R is the quasi-radius of the object. v is the flow velocity relative to the object. The single particle sedimentation procedure was analyzed by the equation of motion,
(Equation S2)
where ρ particle and ρ fluid are the density values of the particle and the fluid, respectively, and g is the gravitational acceleration. Integrating both sides of Equation S2 gives,
(Equation S3)
S-4
To calculate the stability time, t∞ , parameters of v0 and v∞ are needed. The initial injection velocity, v0 , can be obtained, 2 v0tspray ⋅ π rgun = Vspray
(Equation S4)
where tspray is the time consumed for spraying a specific fluidic volume Vspray , and rgun is radius of the spraying gun nozzle. At the equilibrium state, the excess forces of gravity and buoyancy will balance the Stoke’s drag force,
4 Fd = Fg − Fb = ( ρ particle − ρ fluid )⋅ g ⋅ π R3 3
(Equation S5)
The resulting equilibrium velocity, v∞ , can be calculated via combining Equations S1 and S5,
v∞ =
2 ( ρ particle − ρ fluid ) ⋅ g ⋅ R2 9 µ
(Equation S6)
Taking all the equations above, the calculated particle settling time was plotted in Figure S4.
S-5
Figure S4. Relaxation time from vertical to horizontal alignment for a single particle (i.e., diameter of 40 nm and length of 2 µm and viscosity values at shear rate of 631 s-1 were taken from Figure 4) in various viscous fluids used in this research
SIII. Literature research of epoxy composites mechanical properties as compared to this study
Figure S5. Ashby Chart of modulus increase (i.e., %, (Ecomposite-Eepoxy)/Eepoxy) of nanoparticles/epoxy composites vs. particle concentrations. Carbon nanotubes 3-13, graphene 14-25, montmorillonitrile clay 26-30, silica 31-42, and current work data has been plotted. Tilted lines stand for specific modulus increase in percentage, and the slopes indicate reinforcement in modulus per unit particle concentration. It can be seen that the current work showed intermediate reinforcement efficiency between graphene and carbon nanotubes; however, HNTs cost is $2/kg, while carbon nanotubes and graphene price range from $50/g to $500/g43. The current work also achieves modulus increases beyond that from frequently used particles of montmorillonite and silica. The secret is in the particle alignment along loading direction. SIV. Composite mechanics TGA experiments were used to confirm the concentrations of HNT in the final processed composites. Data of this type is compared in Figure 6a with the nominal HNT compositions, based on formulation compounding. It can be seen that the final composite concentrations are very consistent with the designed loadings (Figure 6b). This also validates a stable distribution of HNTs in the various viscous spray-processing formulations, where epoxy/acetone ratios vary considerably. Macroscopic sedimentation
S-6
was not observed even in 10.2 vol% HNT loadings. In Cox-Krenchel model44, length efficiency factor was defined,
tanh(na) ] na 2Gm n= [ ] E f ln(2R / d)
ηl =1−[
a=
(Equation S7) (Equation S8)
l d
(Equation S9)
where Gm is the shear modulus of polymer matrix, 2R is the distance from the fiber to its nearest neighbor fiber, l and d mean the length and diameter of the particle. At fixed fiber concentration below percolation (i.e., less than 1 vol% in our HNT nanocomposites) and under uniform dispersion, length efficiency is only dependent on aspect ratio and concentration as shown in Equations S7 to S9. Figure S6c shows how the length efficiency factor changes with lumped parameter na, and the insert demonstrates how na changes with volume concentrations. Based on this curve from Equation S7, as well as the parameters including ① shear modulus of 1.7 GPa for epoxy as calculated from the experimentally determined Young’s modulus (4.5 GPa), ② Poisson’s ratio (0.3), ③tensile modulus for HNTs of 300 GPa45-46, and ④ HNTs concentration of 0.5 vol.% generate a value of 5 for na. This corresponds to a length efficiency of 81% in Figure S6c. In this study, the HNT volume fractions, Vf, varied from ∼0.5 vol% to ∼10.2 vol%, indicating the matrix volume fractions, Vm, from ∼99.5 vol% to ∼89.8 vol%. This change in concentration, however, does not change the length efficiency factor significantly, with ηl ranges from 81% to 86% (insert in Figure S6c). Therefore, the analysis of orientation efficiency factor will reveal their main influencing effectiveness on mechanical properties as discussed in the manuscript.
S-7
Figure S6 (a) TGA of composites with various HNT concentrations, and (b) the relationship of HNT concentration between experimental design and actual values in the final cured composites showed consistency. (c) Length efficiency factor (ηl) as a function of parameter na. SV.
Orientation of HNT based on composite mechanics
S-8
Figure S7 Contour of composite elastic modulus from Cox-Krenchel model with orientation factor and volume fraction variations. Composite moduli at various volumes (i.e., 0.5 vol% and 1.0 vol%) showed the orientation factor trend distinctively. Composites based on E40A60 (O), E77A23 (☐), E87A13 (✩), E93A7 (∆), and E100A0 (◊) are marked. The orientation factor can also be calculated based on composite mechanics. The spincoating method produces a film with randomly orientated particles with an orientation factor ηo of 0.247. A linear fitting of the experimental modulus values between 0 and 1 vol% in spin-coated films gives effective modulus of HNT of ∼312 GPa (i.e., moduli of 5.20, 5.74, and 5.81 GPa at HNT concentrations of 0, 0.5, and 1.0 vol%). At a rough estimation, Em =4.5 GPa and Ef=312 GPa, the composite modulus relative to orientation factor (i.e., 0 to 1) and fiber volume fraction (i.e., 0 to 1 vol%) is plotted in Figure S7. The spray-coated samples were shown as white symbols on the contour so that their orientation factors at specific volumes of 0.5 vol% and 1.0 vol% become straightforward. The orientation factors showed consistent increase with viscosity values. Figure S7 shows that with a specific volume fraction, better consistency in particle orientation results in high modulus values. In spite of this relationship between orientation factor and modulus values, composite mechanics is not a straightforward method for particle orientation calculations. Therefore statistical quantifications of HNT orientations in these composites are important and have been given in the manuscript discussion sections. Table S1. Orientation factors calculated from composite mechanics Samples Orientation factors based on composite mechanics E40A60 E77A23 E87A13 E93A7 0.5 (vol%) 0.38 N/A 0.46 0.97 1.0 (vol%) 0.72 0.68 0.81 1.00
S-9
E100A0 0.69 0.96
SVI.
Analyses of HNTs alignment based on SEM images
Table S2. Gaussian fitting of halloysite orientations in composite coatings Sample Fitted Gaussian equation parameters Solution HNTs Concentration A FWHM components (vol%) E77A23 0.5 426.72 28.71 1.0 477.15 49.47 4.8 413.50 26.55 10.2 451.45 22.49 E93A7 0.5 504.60 96.76 1.0 484.29 66.70 4.8 496.07 70.93 10.2 458.86 65.17 E100A0 0.5 497.18 58.83 1.0 474.18 44.40 4.8 468.66 26.37 10.2 425.74 15.56 Note: Gaussian fitting of y = y0 +
Ae w
−4 ln(2)( x−xc )2 w2
π
, where yc=y0+A/(FWHM*sqrt(π/4ln2)),
4 ln(2) FWHM is the full width at half maximum and A is the area integrated. y0 is base, xc stands for the fitted peak center which is 0o for out-of-plane aligned particles and 90o for inplane aligned particles. The script access of the function is nlf_Gaussian(x,y0,xc,A,w). SVII.
Intrinsic modulus for halloysite
Table S3. Mechanics of HNT from literature and current work Report Test method Parameters 48 2005 First principle study Kaolinite with halloysite composition shows using molecular Young’s modulus of 170 GPa along tube direction dynamics simulations 201045 Simulation using selfSingle-wall HNT posses moduli between 234 and consistent charge 339 GPa with diameters ranging from 1.7 to 4.6 nm density-functional based tight-binding (SCC-DFTB) method 49 2011 TEM observed Bending moduli ranges from 60 to 156 GPa cantilever beam dependent on radius from 16 to 70 nm bending tests 201346 Three-point bending The calculated average elastic modulus ranges from tests performed on average 10 to 600 GPa, with a diameter-normalized individual nanotubes value of 140 GPa, measured for a set of tubes with using an AFM tip outer diameters ranging between 50 and 160 nm.
S-10
Current work
Composite mechanics
The highest value reaches around 600 GPa at diameters less than 50 nm. Reinforcement modulus without considering misalignment effects reached as high as 182 GPa and HNT intrinsic modulus was predicted to be around 420 GPa
SVIII. Percolation threshold analyses HNT particles have been known for their high modulus, up to around 600 GPa at outer diameters of less than 50 nm. However, as tubes started aggregating, the accumulating defects and the lack of inter-tubular registry resulting from diameter differences and helicity variations will lead to decrease of effective modulus, especially shear modulus. For example, carbon nanotubes have been shown to have shear modulus of 6 GPa for 4.5 nm bundles, 2.3 GPa for 9 nm bundles and 0.7 GPa for 20 nm bundles 50-52. Therefore a theoretical estimation of the average modulus dependent on bundle size will be necessary to understand the plateau region in Figure 9. The average effective modulus <Ex> has been calculated using continuum mechanics (Equation S10)47. Modulus along longitudinal direction (E1), transverse direction (E2), and Poisson’s ratio (ν) were from Table 4 and also listed in Figure 9d. Shear modulus (G12) dependent on bundles size is not available experimentally; here in this research were taken as 2, 5, 10, and 20 GPa to show the average modulus change with bundle size53. The existence of plateau region can be attributed to two aspects. (i) From Figure 9d, it can be seen that with the bundle size increase, the decrease in effective average modulus can be one order of magnitude lower. In addition, for the same bundle size, the average modulus was also found to improve with higher alignment. This is also consistent with the phenomenon as indicated from the trend line in Figures 8a and 8b. (ii) The bundled structure not only influences the intrinsic particle modulus and hardness values but also affect the interaction between polymers and particles. Fully dispersed and exfoliated nanotubes will have more contact area than aggregates, and reinforcement efficiency has also been found to be linearly proportional to interfacial area54. This could be another reason for the formation of plateau.
1 < cos4 θ > < sin 4θ > 1 2ν12 = + +( − ) < cos2 θ cos2 θ > G12 E1 < Ex > E1 E2 1 2ν12 2 1 1 1 2ν12 1 − − ) < cos2 θ > +( + − + ) < cos 4 θ > = +( E2 G12 E1 E2 E1 E2 G12 E1
(Equation S10)
References 1. Liu, Y. J.; Joseph, D. D., Sedimentation of Particles in Polymer Solutions. J. Fluid Mech. 1993, 255, 565-595. 2. Munson, B. R.; Young, D. F.; Okiishi, T. H., Fundamentals of Fluid Mechanics. 2nd ed.; John Wiley & Sons, Inc: New York US, 1990; Vol. 3, p 4-40. 3. Gojny, F. H.; Wichmann, M. H. G.; Fiedler, B.; Schulte, K., Influence of Different Carbon Nanotubes on the Mechanical Properties of Epoxy Matrix Composites – a Comparative Study. Compos. Sci. Technol. 2005, 65, 2300-2313.
S-11
4. Sun, L.; Warren, G. L.; O’Reilly, J. Y.; Everett, W. N.; Lee, S. M.; Davis, D.; Lagoudas, D.; Sue, H. J., Mechanical Properties of Surface-Functionalized Swcnt/Epoxy Composites. Carbon 2008, 46, 320-328. 5. Gojny, F.; Wichmann, M.; Köpke, U.; Fiedler, B.; Schulte, K., Carbon NanotubeReinforced Epoxy-Composites: Enhanced Stiffness and Fracture Toughness at Low Nanotube Content. Compos. Sci. Technol. 2004, 64, 2363-2371. 6. Ayatollahi, M. R.; Shadlou, S.; Shokrieh, M. M., Fracture Toughness of Epoxy/Multi-Walled Carbon Nanotube Nano-Composites under Bending and Shear Loading Conditions. Mater. Des. 2011, 32, 2115-2124. 7. Ayatollahi, M. R.; Shadlou, S.; Shokrieh, M. M., Mixed Mode Brittle Fracture in Epoxy/Multi-Walled Carbon Nanotube Nanocomposites. Eng. Fract. Mech. 2011, 78, 2620-2632. 8. Young, R. J.; Kinloch, I. A.; Gong, L.; Novoselov, K. S., The Mechanics of Graphene Nanocomposites: A Review. Compos. Sci. Technol. 2012, 72, 1459-1476. 9. Gkikas, G.; Barkoula, N. M.; Paipetis, A. S., Effect of Dispersion Conditions on the Thermo-Mechanical and Toughness Properties of Multi Walled Carbon Nanotubes-Reinforced Epoxy. Composites, Part B 2012, 43, 2697-2705. 10. Tang, L.-c.; Zhang, H.; Han, J.-h.; Wu, X.-p.; Zhang, Z., Fracture Mechanisms of Epoxy Filled with Ozone Functionalized Multi-Wall Carbon Nanotubes. Compos. Sci. Technol. 2011, 72, 7-13. 11. Karapappas, P.; Vavouliotis, A.; Tsotra, P.; Kostopoulos, V.; Palpetis, A., Enhanced Fracture Properties of Carbon Reinforced Composites by the Addition of Multi-Wall Carbon Nanotubes. J. Compos. Mater. 2009, 43, 977-985. 12. Hsieh, T. H.; Kinloch, A. J.; Taylor, A. C.; Kinloch, I. A., The Effect of Carbon Nanotubes on the Fracture Toughness and Fatigue Performance of a Thermosetting Epoxy Polymer. J. Mater. Sci. 2011, 46, 7525-7535. 13. Hsieh, T.; Kinloch, A.; Taylor, A.; Sprenger, S., The Effect of Silica Nanoparticles and Carbon Nanotubes on the Toughness of a Thermosetting Epoxy Polymer. J. Appl. Polym. Sci. 2011, 119, 2135-2142. 14. Liu, Y.; Wu, H.; Chen, G., Enhanced Mechanical Properties of Nanocomposites at Low Graphene Content Based on in Situ Ball Milling. Polym. Compos. 2014, 37, 1190-1197. 15. Tang, L.-C.; Wan, Y.-J.; Yan, D.; Pei, Y.-B.; Zhao, L.; Li, Y.-B.; Wu, L.-B.; Jiang, J.X.; Lai, G.-Q., The Effect of Graphene Dispersion on the Mechanical Properties of Graphene/Epoxy Composites. Carbon 2013, 60, 16-27. 16. Bortz, D. R.; Heras, E. G.; Martin-Gullon, I., Impressive Fatigue Life and Fracture Toughness Improvements in Graphene Oxide/Epoxy Composites. Macromol. 2012, 45, 238-245. 17. Zaman, I.; Phan, T. T.; Kuan, H.-C.; Meng, Q.; Bao La, L. T.; Luong, L.; Youssf, O.; Ma, J., Epoxy/Graphene Platelets Nanocomposites with Two Levels of Interface Strength. Polym. 2011, 52, 1603-1611. 18. Zaman, I.; Kuan, H. C.; Meng, Q.; Michelmore, A.; Kawashima, N.; Pitt, T.; Zhang, L.; Gouda, S.; Luong, L.; Ma, J., A Facile Approach to Chemically Modified Graphene and Its Polymer Nanocomposites. Adv. Funct. Mater. 2012, 22, 2735-2743. 19. Chatterjee, S.; Wang, J. W.; Kuo, W. S.; Tai, N. H.; Salzmann, C.; Li, W. L.; Hollertz, R.; Nüesch, F. A.; Chu, B. T. T., Mechanical Reinforcement and Thermal S-12
Conductivity in Expanded Graphene Nanoplatelets Reinforced Epoxy Composites. Chem. Phys. Lett. 2012, 531, 6-10. 20. Jiang, T.; Kuila, T.; Kim, N. H.; Ku, B.-C.; Lee, J. H., Enhanced Mechanical Properties of Silanized Silica Nanoparticle Attached Graphene Oxide/Epoxy Composites. Compos. Sci. Technol. 2013, 79, 115-125. 21. Shokrieh, M. M.; Ghoreishi, S. M.; Esmkhani, M.; Zhao, Z., Effects of Graphene Nanoplatelets and Graphene Nanosheets on Fracture Toughness of Epoxy Nanocomposites. Fatigue Fract. Eng. Mater. Struct. 2014, 37, 1116-1123. 22. Li, Z.; Wang, R.; Young, R. J.; Deng, L.; Yang, F.; Hao, L.; Jiao, W.; Liu, W., Control of the Functionality of Graphene Oxide for Its Application In epoxy Nanocomposites. Polym. 2013, 54, 6437-6446. 23. Chandrasekaran, S.; Sato, N.; Tölle, F.; Mülhaupt, R.; Fiedler, B.; Schulte, K., Fracture Toughness and Failure Mechanism of Graphene Based Epoxy Composites. Compos. Sci. Technol. 2014, 97, 90-99. 24. Ahmadi-Moghadam, B.; Taheri, F., Fracture and Toughening Mechanisms of Gnp-Based Nanocomposites in Modes I and Ii Fracture. Eng. Fract. Mech. 2014, 131, 329-339. 25. Galpaya, D.; Wang, M.; Liu, M.; Motta, N.; Waclawik, E.; Yan, C., Recent Advances in Fabrication and Characterization of Graphene-Polymer Nanocomposites. Graphene 2012, 1, 30-49. 26. Qi, B.; Zhang, Q. X.; Bannister, M.; Mai, Y. W., Investigation of the Mechanical Properties of Dgeba-Based Epoxy Resin with Nanoclay Additives. Compos. Struct. 2006, 75, 514-519. 27. Wang, L.; Wang, K.; Chen, L.; Zhang, Y.; He, C., Preparation, Morphology and Thermal/Mechanical Pproperties of Epoxy/Nanoclay Composite. Composites, Part A 2006, 37, 1890-1896. 28. Wang, K.; Chen, L.; Wu, J.; Toh, M. L.; He, C.; Yee, A. F., Epoxy Nanocomposites with Highly Exfoliated Clay: Mechanical Properties and Fracture Mechanisms. Macromol. 2005, 38, 788-800. 29. Zappalorto, M.; Salviato, M.; Quaresimin, M., Mixed Mode (I + Ii) Fracture Toughness of Polymer Nanoclay Nanocomposites. Eng. Fract. Mech. 2013, 111, 5064. 30. Guevara-Morales, A.; Taylor, A. C., Mechanical and Dielectric Properties of Epoxy–Clay Nanocomposites. J. Mater. Sci. 2013, 49, 1574-1584. 31. Tang, L.-C.; Zhang, H.; Sprenger, S.; Ye, L.; Zhang, Z., Fracture Mechanisms of Epoxy-Based Ternary Composites Filled with Rigid-Soft Particles. Compos. Sci. Technol. 2012, 72, 558-565. 32. Liu, H.-Y.; Wang, G.-T.; Mai, Y.-W.; Zeng, Y., On Fracture Toughness of NanoParticle Modified Epoxy. Composites, Part B 2011, 42, 2170-2175. 33. Brunner, A. J.; Necola, A.; Rees, M.; Gasser, P.; Kornmann, X.; Thomann, R.; Barbezat, M., The Influence of Silicate-Based Nano-Filler on the Fracture Toughness of Epoxy Resin. Eng. Fract. Mech. 2006, 73, 2336-2345. 34. Chen, L.; Chai, S.; Liu, K.; Ning, N.; Gao, J.; Liu, Q.; Chen, F.; Fu, Q., Enhanced Epoxy/Silica Composites Mechanical Properties by Introducing Graphene Oxide to the Interface. ACS Appl. Mater. Interfaces 2012, 4, 4398-4404.
S-13
35. Liang, Y. L.; Pearson, R. A., Toughening Mechanisms in Epoxy–Silica Nanocomposites (Esns). Polym. 2009, 50, 4895-4905. 36. Zhang, C.; Wang, J.; Du, Y.; Zhang, W., An Investigation on the Thermodynamic Stability of V6si5. J. Mater. Sci. 2007, 42, 7046-7048. 37. Kinloch, A. J.; Mohammed, R. D.; Taylor, A. C.; Eger, C.; Sprenger, S.; Egan, D., The Effect of Silica Nano Particles and Rubber Particles on the Tughness of Multiphase Thermosetting Epoxy Polymers. J. Mater. Sci. 2005, 40, 5083-5086. 38. Zamanian, M.; Mortezaei, M.; Salehnia, B.; Jam, J. E., Fracture Toughness of Epoxy Polymer Modified with Nanosilica Particles: Particle Size Effect. Eng. Fract. Mech. 2013, 97, 193-206. 39. Dittanet, P.; Pearson, R. A., Effect of Silica Nanoparticle Size on Toughening Mechanisms of Filled Epoxy. Polym. 2012, 53, 1890-1905. 40. Johnsen, B. B.; Kinloch, A. J.; Mohammed, R. D.; Taylor, A. C.; Sprenger, S., Toughening Mechanisms of Nanoparticle-Modified Epoxy Polymers. Polym. 2007, 48, 530-541. 41. Bray, D. J.; Dittanet, P.; Guild, F. J.; Kinloch, A. J.; Masania, K.; Pearson, R. A.; Taylor, A. C., The Modelling of the Toughening of Epoxy Polymers Via Silica Nanoparticles: The Effects of Volume Fraction and Particle Size. Polym. 2013, 54, 7022-7032. 42. Ma, J.; Mo, M.-S.; Du, X.-S.; Rosso, P.; Friedrich, K.; Kuan, H.-C., Effect of Inorganic Nanoparticles on Mechanical Property, Fracture Toughness and Toughening Mechanism of Two Epoxy Systems. Polym. 2008, 49, 3510-3523. 43. Https://Www.Cheaptubes.Com. 44. Cox, H., The Elasticity and Strength of Paper and Other Fibrous Materials. Br. J. Appl. Phys. 1952, 3, 72-75. 45. Guimaraes, L.; Enyashin, A. N.; Seifert, G.; Duarte, H. A., Structural, Electronic, and Mechanical Properties of Single-Walled Halloysite Nanotube Models. J. Phys. Chem. C 2010, 114, 11358-11363. 46. Lecouvet, B.; Horion, J.; D’Haese, C.; Bailly, C.; Nysten, B., Elastic Modulus of Halloysite Nanotubes. Nanotech. 2013, 24, 105704-105711. 47. Song, K.; Zhang, Y.; Meng, J.; Green, E. C.; Tajaddod, N.; Li, H.; Minus, M. L., Structural Polymer-Based Carbon Nanotube Composite Fibers: Understanding the Processing–Structure–Performance Relationship. Mater. 2013, 6, 2543-2577. 48. Sato, H.; Ono, K.; Johnston, C. T.; Yamagishi, A., First-Principles Studies on the Elastic Constants of a 1: 1 Layered Kaolinite Mineral. Am. Mineral. 2005, 90, 18241826. 49. Lu, D.; Chen, H.; Wu, J.; Chan, C. M., Direct Measurements of the Young's Modulus of a Single Halloysite Nanotube Using a Transmission Electron Microscope with a Bending Stage. J. Nanosci. Nanotechnol. 2011, 11, 7789-7793. 50. Salvetat, J.-P.; Briggs, G. A. D.; Bonard, J.-M.; Bacsa, R. R.; Kulik, A. J.; Stöckli, T.; Burnham, N. A.; Forró, L., Elastic and Shear Moduli of Single-Walled Carbon Nanotube Ropes. Phys. Rev. Lett. 1999, 82, 944-947. 51. Satcurada, I.; Ito, T.; Nakamae, K., Elastic Moduli of the Crystal Lattices of Polymers. J. Polym. Sci., Part C: Polym. Symp. 1967, 15, 75-91. 52. Popov, V.; Van Doren, V.; Balkanski, M., Elastic Properties of Crystals of Single-Walled Carbon Nanotubes. Solid State Commun. 2000, 114, 395-399. S-14
53. Liu, T.; Kumar, S., Effect of Orientation on the Modulus of Swnt Films and Fibers. Nano Lett. 2003, 3, 647-650. 54. Cadek, M.; Coleman, J. N.; Ryan, K. P., Reinforcement of Polymers with Carbon Nanotubes:The Role of Nanotube Surface Area. Nano Lett. 2004, 4, 353-356.
S-15
‡,*
, Robert E. Cohen
Department of Materials Science and Engineering, Department of Chemical Engineering, and Department of Mechanical Engineering, MIT, 77 Mass Ave, Cambridge, MA, USA, 02139. ‡,* TDK Professor of Polymer Materials Science and Engineering, and Director of CMSE, MIT, 77 Mass Ave, Cambridge, MA, USA, 02139. Correspondence email: [email protected] §,* St. Laurent Professor of Chemical Engineering Department, MIT, 77 Mass Ave, Cambridge, MA, USA, 02139. Correspondence email: [email protected] ◊,* Department of Materials Science and Engineering, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates. Correspondence email: [email protected]
S-1
SI. Viscosity measurements from rheometer
Figure S1. Viscosity vs. shear rate for HNT suspensions in E40A60, E77A23, E87A13, E93A7 and E100A0, showed an increasing viscosity trend with higher epoxy content. The concentration of HNTs in each figure remains constant. The particle concentration only slightly affects the viscosity compared to the significant change caused by the percentage
S-2
of epoxy added. The shear rates in the rheometer measurements are from 10 to 1000 s-1 and the temperature is set at 23 oC. SII. Relaxation time for nanotubes in fluids Shear-aligned halloysite nanotubes were sprayed on a glass slide. The alignment of nanotubes is constrained by the epoxy and given enough time the nanotubes would lose their alignment and reach a state of relaxation. The tilted angle and rate depend on particle features (i.e., length, density, shape), and liquid characteristics (i.e., viscosity, temperature, pressure)1. The fluid consisting of either pure epoxy or different epoxy/acetone mixtures all displayed Newtonian behavior, as shown in Figure S2. The orientation of the body would eventually be determined by inertia1. Bodies with force and front-end symmetry were torque free when settling in Stokes flow, so that the torques due to inertia were unopposed. This resulted in an eventual out-of-plane orientation for all particles1.
Figure S2. Shear stress as a function of shear rates for (a) E100A0 and (b) E93A7 based composites. Linear trends between shear force and shear rate are observed, which exhibits the characteristic of Newtonian fluids. E87A13, E77A23 and E40A60 display the same Newtonian liquid behavior due to the increase in acetone concentration.
S-3
Figure S3. Schematic shows the single halloysite nanotube states of (i) as-ejected into the coating surface, and (ii) reaching steady state, and micromechanics model. Relative flow motion past a falling particle in a fluid (i.e., a halloysite nanotube falling through the epoxy solution or melt) generates drag force, Fd, force due to gravity, Fg, as well as buoyancy, Fb. The sedimentation of the tubes until reaching steady state is equivalent to the steady flow past a stationary long body of halloysite. To simplify the problem, the micromechanics analysis model for a single HNT particle (i.e., diameter of 40 nm and length of 2 µm) falling in a viscous fluid (i.e., viscosity taken from Figure 4) was plotted in Figure S3. The time for the tube to reach steady in-plane state was calculated based on this micromechanics model (Figure S3). According to Stoke’s Law, the force of viscosity on a small particle moving through a viscous fluid is given by2,
Fd = 6πµ Rv
(Equation S1)
where Fd is the friction force, known as Stoke’s drag, acting on the interface between the fluid and particle. µ is the dynamic viscosity. The liquid states studied here are all Newtonian fluids. Viscosity values were taken as a constant from experimental measurements. R is the quasi-radius of the object. v is the flow velocity relative to the object. The single particle sedimentation procedure was analyzed by the equation of motion,
(Equation S2)
where ρ particle and ρ fluid are the density values of the particle and the fluid, respectively, and g is the gravitational acceleration. Integrating both sides of Equation S2 gives,
(Equation S3)
S-4
To calculate the stability time, t∞ , parameters of v0 and v∞ are needed. The initial injection velocity, v0 , can be obtained, 2 v0tspray ⋅ π rgun = Vspray
(Equation S4)
where tspray is the time consumed for spraying a specific fluidic volume Vspray , and rgun is radius of the spraying gun nozzle. At the equilibrium state, the excess forces of gravity and buoyancy will balance the Stoke’s drag force,
4 Fd = Fg − Fb = ( ρ particle − ρ fluid )⋅ g ⋅ π R3 3
(Equation S5)
The resulting equilibrium velocity, v∞ , can be calculated via combining Equations S1 and S5,
v∞ =
2 ( ρ particle − ρ fluid ) ⋅ g ⋅ R2 9 µ
(Equation S6)
Taking all the equations above, the calculated particle settling time was plotted in Figure S4.
S-5
Figure S4. Relaxation time from vertical to horizontal alignment for a single particle (i.e., diameter of 40 nm and length of 2 µm and viscosity values at shear rate of 631 s-1 were taken from Figure 4) in various viscous fluids used in this research
SIII. Literature research of epoxy composites mechanical properties as compared to this study
Figure S5. Ashby Chart of modulus increase (i.e., %, (Ecomposite-Eepoxy)/Eepoxy) of nanoparticles/epoxy composites vs. particle concentrations. Carbon nanotubes 3-13, graphene 14-25, montmorillonitrile clay 26-30, silica 31-42, and current work data has been plotted. Tilted lines stand for specific modulus increase in percentage, and the slopes indicate reinforcement in modulus per unit particle concentration. It can be seen that the current work showed intermediate reinforcement efficiency between graphene and carbon nanotubes; however, HNTs cost is $2/kg, while carbon nanotubes and graphene price range from $50/g to $500/g43. The current work also achieves modulus increases beyond that from frequently used particles of montmorillonite and silica. The secret is in the particle alignment along loading direction. SIV. Composite mechanics TGA experiments were used to confirm the concentrations of HNT in the final processed composites. Data of this type is compared in Figure 6a with the nominal HNT compositions, based on formulation compounding. It can be seen that the final composite concentrations are very consistent with the designed loadings (Figure 6b). This also validates a stable distribution of HNTs in the various viscous spray-processing formulations, where epoxy/acetone ratios vary considerably. Macroscopic sedimentation
S-6
was not observed even in 10.2 vol% HNT loadings. In Cox-Krenchel model44, length efficiency factor was defined,
tanh(na) ] na 2Gm n= [ ] E f ln(2R / d)
ηl =1−[
a=
(Equation S7) (Equation S8)
l d
(Equation S9)
where Gm is the shear modulus of polymer matrix, 2R is the distance from the fiber to its nearest neighbor fiber, l and d mean the length and diameter of the particle. At fixed fiber concentration below percolation (i.e., less than 1 vol% in our HNT nanocomposites) and under uniform dispersion, length efficiency is only dependent on aspect ratio and concentration as shown in Equations S7 to S9. Figure S6c shows how the length efficiency factor changes with lumped parameter na, and the insert demonstrates how na changes with volume concentrations. Based on this curve from Equation S7, as well as the parameters including ① shear modulus of 1.7 GPa for epoxy as calculated from the experimentally determined Young’s modulus (4.5 GPa), ② Poisson’s ratio (0.3), ③tensile modulus for HNTs of 300 GPa45-46, and ④ HNTs concentration of 0.5 vol.% generate a value of 5 for na. This corresponds to a length efficiency of 81% in Figure S6c. In this study, the HNT volume fractions, Vf, varied from ∼0.5 vol% to ∼10.2 vol%, indicating the matrix volume fractions, Vm, from ∼99.5 vol% to ∼89.8 vol%. This change in concentration, however, does not change the length efficiency factor significantly, with ηl ranges from 81% to 86% (insert in Figure S6c). Therefore, the analysis of orientation efficiency factor will reveal their main influencing effectiveness on mechanical properties as discussed in the manuscript.
S-7
Figure S6 (a) TGA of composites with various HNT concentrations, and (b) the relationship of HNT concentration between experimental design and actual values in the final cured composites showed consistency. (c) Length efficiency factor (ηl) as a function of parameter na. SV.
Orientation of HNT based on composite mechanics
S-8
Figure S7 Contour of composite elastic modulus from Cox-Krenchel model with orientation factor and volume fraction variations. Composite moduli at various volumes (i.e., 0.5 vol% and 1.0 vol%) showed the orientation factor trend distinctively. Composites based on E40A60 (O), E77A23 (☐), E87A13 (✩), E93A7 (∆), and E100A0 (◊) are marked. The orientation factor can also be calculated based on composite mechanics. The spincoating method produces a film with randomly orientated particles with an orientation factor ηo of 0.247. A linear fitting of the experimental modulus values between 0 and 1 vol% in spin-coated films gives effective modulus of HNT of ∼312 GPa (i.e., moduli of 5.20, 5.74, and 5.81 GPa at HNT concentrations of 0, 0.5, and 1.0 vol%). At a rough estimation, Em =4.5 GPa and Ef=312 GPa, the composite modulus relative to orientation factor (i.e., 0 to 1) and fiber volume fraction (i.e., 0 to 1 vol%) is plotted in Figure S7. The spray-coated samples were shown as white symbols on the contour so that their orientation factors at specific volumes of 0.5 vol% and 1.0 vol% become straightforward. The orientation factors showed consistent increase with viscosity values. Figure S7 shows that with a specific volume fraction, better consistency in particle orientation results in high modulus values. In spite of this relationship between orientation factor and modulus values, composite mechanics is not a straightforward method for particle orientation calculations. Therefore statistical quantifications of HNT orientations in these composites are important and have been given in the manuscript discussion sections. Table S1. Orientation factors calculated from composite mechanics Samples Orientation factors based on composite mechanics E40A60 E77A23 E87A13 E93A7 0.5 (vol%) 0.38 N/A 0.46 0.97 1.0 (vol%) 0.72 0.68 0.81 1.00
S-9
E100A0 0.69 0.96
SVI.
Analyses of HNTs alignment based on SEM images
Table S2. Gaussian fitting of halloysite orientations in composite coatings Sample Fitted Gaussian equation parameters Solution HNTs Concentration A FWHM components (vol%) E77A23 0.5 426.72 28.71 1.0 477.15 49.47 4.8 413.50 26.55 10.2 451.45 22.49 E93A7 0.5 504.60 96.76 1.0 484.29 66.70 4.8 496.07 70.93 10.2 458.86 65.17 E100A0 0.5 497.18 58.83 1.0 474.18 44.40 4.8 468.66 26.37 10.2 425.74 15.56 Note: Gaussian fitting of y = y0 +
Ae w
−4 ln(2)( x−xc )2 w2
π
, where yc=y0+A/(FWHM*sqrt(π/4ln2)),
4 ln(2) FWHM is the full width at half maximum and A is the area integrated. y0 is base, xc stands for the fitted peak center which is 0o for out-of-plane aligned particles and 90o for inplane aligned particles. The script access of the function is nlf_Gaussian(x,y0,xc,A,w). SVII.
Intrinsic modulus for halloysite
Table S3. Mechanics of HNT from literature and current work Report Test method Parameters 48 2005 First principle study Kaolinite with halloysite composition shows using molecular Young’s modulus of 170 GPa along tube direction dynamics simulations 201045 Simulation using selfSingle-wall HNT posses moduli between 234 and consistent charge 339 GPa with diameters ranging from 1.7 to 4.6 nm density-functional based tight-binding (SCC-DFTB) method 49 2011 TEM observed Bending moduli ranges from 60 to 156 GPa cantilever beam dependent on radius from 16 to 70 nm bending tests 201346 Three-point bending The calculated average elastic modulus ranges from tests performed on average 10 to 600 GPa, with a diameter-normalized individual nanotubes value of 140 GPa, measured for a set of tubes with using an AFM tip outer diameters ranging between 50 and 160 nm.
S-10
Current work
Composite mechanics
The highest value reaches around 600 GPa at diameters less than 50 nm. Reinforcement modulus without considering misalignment effects reached as high as 182 GPa and HNT intrinsic modulus was predicted to be around 420 GPa
SVIII. Percolation threshold analyses HNT particles have been known for their high modulus, up to around 600 GPa at outer diameters of less than 50 nm. However, as tubes started aggregating, the accumulating defects and the lack of inter-tubular registry resulting from diameter differences and helicity variations will lead to decrease of effective modulus, especially shear modulus. For example, carbon nanotubes have been shown to have shear modulus of 6 GPa for 4.5 nm bundles, 2.3 GPa for 9 nm bundles and 0.7 GPa for 20 nm bundles 50-52. Therefore a theoretical estimation of the average modulus dependent on bundle size will be necessary to understand the plateau region in Figure 9. The average effective modulus <Ex> has been calculated using continuum mechanics (Equation S10)47. Modulus along longitudinal direction (E1), transverse direction (E2), and Poisson’s ratio (ν) were from Table 4 and also listed in Figure 9d. Shear modulus (G12) dependent on bundles size is not available experimentally; here in this research were taken as 2, 5, 10, and 20 GPa to show the average modulus change with bundle size53. The existence of plateau region can be attributed to two aspects. (i) From Figure 9d, it can be seen that with the bundle size increase, the decrease in effective average modulus can be one order of magnitude lower. In addition, for the same bundle size, the average modulus was also found to improve with higher alignment. This is also consistent with the phenomenon as indicated from the trend line in Figures 8a and 8b. (ii) The bundled structure not only influences the intrinsic particle modulus and hardness values but also affect the interaction between polymers and particles. Fully dispersed and exfoliated nanotubes will have more contact area than aggregates, and reinforcement efficiency has also been found to be linearly proportional to interfacial area54. This could be another reason for the formation of plateau.
1 < cos4 θ > < sin 4θ > 1 2ν12 = + +( − ) < cos2 θ cos2 θ > G12 E1 < Ex > E1 E2 1 2ν12 2 1 1 1 2ν12 1 − − ) < cos2 θ > +( + − + ) < cos 4 θ > = +( E2 G12 E1 E2 E1 E2 G12 E1
(Equation S10)
References 1. Liu, Y. J.; Joseph, D. D., Sedimentation of Particles in Polymer Solutions. J. Fluid Mech. 1993, 255, 565-595. 2. Munson, B. R.; Young, D. F.; Okiishi, T. H., Fundamentals of Fluid Mechanics. 2nd ed.; John Wiley & Sons, Inc: New York US, 1990; Vol. 3, p 4-40. 3. Gojny, F. H.; Wichmann, M. H. G.; Fiedler, B.; Schulte, K., Influence of Different Carbon Nanotubes on the Mechanical Properties of Epoxy Matrix Composites – a Comparative Study. Compos. Sci. Technol. 2005, 65, 2300-2313.
S-11
4. Sun, L.; Warren, G. L.; O’Reilly, J. Y.; Everett, W. N.; Lee, S. M.; Davis, D.; Lagoudas, D.; Sue, H. J., Mechanical Properties of Surface-Functionalized Swcnt/Epoxy Composites. Carbon 2008, 46, 320-328. 5. Gojny, F.; Wichmann, M.; Köpke, U.; Fiedler, B.; Schulte, K., Carbon NanotubeReinforced Epoxy-Composites: Enhanced Stiffness and Fracture Toughness at Low Nanotube Content. Compos. Sci. Technol. 2004, 64, 2363-2371. 6. Ayatollahi, M. R.; Shadlou, S.; Shokrieh, M. M., Fracture Toughness of Epoxy/Multi-Walled Carbon Nanotube Nano-Composites under Bending and Shear Loading Conditions. Mater. Des. 2011, 32, 2115-2124. 7. Ayatollahi, M. R.; Shadlou, S.; Shokrieh, M. M., Mixed Mode Brittle Fracture in Epoxy/Multi-Walled Carbon Nanotube Nanocomposites. Eng. Fract. Mech. 2011, 78, 2620-2632. 8. Young, R. J.; Kinloch, I. A.; Gong, L.; Novoselov, K. S., The Mechanics of Graphene Nanocomposites: A Review. Compos. Sci. Technol. 2012, 72, 1459-1476. 9. Gkikas, G.; Barkoula, N. M.; Paipetis, A. S., Effect of Dispersion Conditions on the Thermo-Mechanical and Toughness Properties of Multi Walled Carbon Nanotubes-Reinforced Epoxy. Composites, Part B 2012, 43, 2697-2705. 10. Tang, L.-c.; Zhang, H.; Han, J.-h.; Wu, X.-p.; Zhang, Z., Fracture Mechanisms of Epoxy Filled with Ozone Functionalized Multi-Wall Carbon Nanotubes. Compos. Sci. Technol. 2011, 72, 7-13. 11. Karapappas, P.; Vavouliotis, A.; Tsotra, P.; Kostopoulos, V.; Palpetis, A., Enhanced Fracture Properties of Carbon Reinforced Composites by the Addition of Multi-Wall Carbon Nanotubes. J. Compos. Mater. 2009, 43, 977-985. 12. Hsieh, T. H.; Kinloch, A. J.; Taylor, A. C.; Kinloch, I. A., The Effect of Carbon Nanotubes on the Fracture Toughness and Fatigue Performance of a Thermosetting Epoxy Polymer. J. Mater. Sci. 2011, 46, 7525-7535. 13. Hsieh, T.; Kinloch, A.; Taylor, A.; Sprenger, S., The Effect of Silica Nanoparticles and Carbon Nanotubes on the Toughness of a Thermosetting Epoxy Polymer. J. Appl. Polym. Sci. 2011, 119, 2135-2142. 14. Liu, Y.; Wu, H.; Chen, G., Enhanced Mechanical Properties of Nanocomposites at Low Graphene Content Based on in Situ Ball Milling. Polym. Compos. 2014, 37, 1190-1197. 15. Tang, L.-C.; Wan, Y.-J.; Yan, D.; Pei, Y.-B.; Zhao, L.; Li, Y.-B.; Wu, L.-B.; Jiang, J.X.; Lai, G.-Q., The Effect of Graphene Dispersion on the Mechanical Properties of Graphene/Epoxy Composites. Carbon 2013, 60, 16-27. 16. Bortz, D. R.; Heras, E. G.; Martin-Gullon, I., Impressive Fatigue Life and Fracture Toughness Improvements in Graphene Oxide/Epoxy Composites. Macromol. 2012, 45, 238-245. 17. Zaman, I.; Phan, T. T.; Kuan, H.-C.; Meng, Q.; Bao La, L. T.; Luong, L.; Youssf, O.; Ma, J., Epoxy/Graphene Platelets Nanocomposites with Two Levels of Interface Strength. Polym. 2011, 52, 1603-1611. 18. Zaman, I.; Kuan, H. C.; Meng, Q.; Michelmore, A.; Kawashima, N.; Pitt, T.; Zhang, L.; Gouda, S.; Luong, L.; Ma, J., A Facile Approach to Chemically Modified Graphene and Its Polymer Nanocomposites. Adv. Funct. Mater. 2012, 22, 2735-2743. 19. Chatterjee, S.; Wang, J. W.; Kuo, W. S.; Tai, N. H.; Salzmann, C.; Li, W. L.; Hollertz, R.; Nüesch, F. A.; Chu, B. T. T., Mechanical Reinforcement and Thermal S-12
Conductivity in Expanded Graphene Nanoplatelets Reinforced Epoxy Composites. Chem. Phys. Lett. 2012, 531, 6-10. 20. Jiang, T.; Kuila, T.; Kim, N. H.; Ku, B.-C.; Lee, J. H., Enhanced Mechanical Properties of Silanized Silica Nanoparticle Attached Graphene Oxide/Epoxy Composites. Compos. Sci. Technol. 2013, 79, 115-125. 21. Shokrieh, M. M.; Ghoreishi, S. M.; Esmkhani, M.; Zhao, Z., Effects of Graphene Nanoplatelets and Graphene Nanosheets on Fracture Toughness of Epoxy Nanocomposites. Fatigue Fract. Eng. Mater. Struct. 2014, 37, 1116-1123. 22. Li, Z.; Wang, R.; Young, R. J.; Deng, L.; Yang, F.; Hao, L.; Jiao, W.; Liu, W., Control of the Functionality of Graphene Oxide for Its Application In epoxy Nanocomposites. Polym. 2013, 54, 6437-6446. 23. Chandrasekaran, S.; Sato, N.; Tölle, F.; Mülhaupt, R.; Fiedler, B.; Schulte, K., Fracture Toughness and Failure Mechanism of Graphene Based Epoxy Composites. Compos. Sci. Technol. 2014, 97, 90-99. 24. Ahmadi-Moghadam, B.; Taheri, F., Fracture and Toughening Mechanisms of Gnp-Based Nanocomposites in Modes I and Ii Fracture. Eng. Fract. Mech. 2014, 131, 329-339. 25. Galpaya, D.; Wang, M.; Liu, M.; Motta, N.; Waclawik, E.; Yan, C., Recent Advances in Fabrication and Characterization of Graphene-Polymer Nanocomposites. Graphene 2012, 1, 30-49. 26. Qi, B.; Zhang, Q. X.; Bannister, M.; Mai, Y. W., Investigation of the Mechanical Properties of Dgeba-Based Epoxy Resin with Nanoclay Additives. Compos. Struct. 2006, 75, 514-519. 27. Wang, L.; Wang, K.; Chen, L.; Zhang, Y.; He, C., Preparation, Morphology and Thermal/Mechanical Pproperties of Epoxy/Nanoclay Composite. Composites, Part A 2006, 37, 1890-1896. 28. Wang, K.; Chen, L.; Wu, J.; Toh, M. L.; He, C.; Yee, A. F., Epoxy Nanocomposites with Highly Exfoliated Clay: Mechanical Properties and Fracture Mechanisms. Macromol. 2005, 38, 788-800. 29. Zappalorto, M.; Salviato, M.; Quaresimin, M., Mixed Mode (I + Ii) Fracture Toughness of Polymer Nanoclay Nanocomposites. Eng. Fract. Mech. 2013, 111, 5064. 30. Guevara-Morales, A.; Taylor, A. C., Mechanical and Dielectric Properties of Epoxy–Clay Nanocomposites. J. Mater. Sci. 2013, 49, 1574-1584. 31. Tang, L.-C.; Zhang, H.; Sprenger, S.; Ye, L.; Zhang, Z., Fracture Mechanisms of Epoxy-Based Ternary Composites Filled with Rigid-Soft Particles. Compos. Sci. Technol. 2012, 72, 558-565. 32. Liu, H.-Y.; Wang, G.-T.; Mai, Y.-W.; Zeng, Y., On Fracture Toughness of NanoParticle Modified Epoxy. Composites, Part B 2011, 42, 2170-2175. 33. Brunner, A. J.; Necola, A.; Rees, M.; Gasser, P.; Kornmann, X.; Thomann, R.; Barbezat, M., The Influence of Silicate-Based Nano-Filler on the Fracture Toughness of Epoxy Resin. Eng. Fract. Mech. 2006, 73, 2336-2345. 34. Chen, L.; Chai, S.; Liu, K.; Ning, N.; Gao, J.; Liu, Q.; Chen, F.; Fu, Q., Enhanced Epoxy/Silica Composites Mechanical Properties by Introducing Graphene Oxide to the Interface. ACS Appl. Mater. Interfaces 2012, 4, 4398-4404.
S-13
35. Liang, Y. L.; Pearson, R. A., Toughening Mechanisms in Epoxy–Silica Nanocomposites (Esns). Polym. 2009, 50, 4895-4905. 36. Zhang, C.; Wang, J.; Du, Y.; Zhang, W., An Investigation on the Thermodynamic Stability of V6si5. J. Mater. Sci. 2007, 42, 7046-7048. 37. Kinloch, A. J.; Mohammed, R. D.; Taylor, A. C.; Eger, C.; Sprenger, S.; Egan, D., The Effect of Silica Nano Particles and Rubber Particles on the Tughness of Multiphase Thermosetting Epoxy Polymers. J. Mater. Sci. 2005, 40, 5083-5086. 38. Zamanian, M.; Mortezaei, M.; Salehnia, B.; Jam, J. E., Fracture Toughness of Epoxy Polymer Modified with Nanosilica Particles: Particle Size Effect. Eng. Fract. Mech. 2013, 97, 193-206. 39. Dittanet, P.; Pearson, R. A., Effect of Silica Nanoparticle Size on Toughening Mechanisms of Filled Epoxy. Polym. 2012, 53, 1890-1905. 40. Johnsen, B. B.; Kinloch, A. J.; Mohammed, R. D.; Taylor, A. C.; Sprenger, S., Toughening Mechanisms of Nanoparticle-Modified Epoxy Polymers. Polym. 2007, 48, 530-541. 41. Bray, D. J.; Dittanet, P.; Guild, F. J.; Kinloch, A. J.; Masania, K.; Pearson, R. A.; Taylor, A. C., The Modelling of the Toughening of Epoxy Polymers Via Silica Nanoparticles: The Effects of Volume Fraction and Particle Size. Polym. 2013, 54, 7022-7032. 42. Ma, J.; Mo, M.-S.; Du, X.-S.; Rosso, P.; Friedrich, K.; Kuan, H.-C., Effect of Inorganic Nanoparticles on Mechanical Property, Fracture Toughness and Toughening Mechanism of Two Epoxy Systems. Polym. 2008, 49, 3510-3523. 43. Https://Www.Cheaptubes.Com. 44. Cox, H., The Elasticity and Strength of Paper and Other Fibrous Materials. Br. J. Appl. Phys. 1952, 3, 72-75. 45. Guimaraes, L.; Enyashin, A. N.; Seifert, G.; Duarte, H. A., Structural, Electronic, and Mechanical Properties of Single-Walled Halloysite Nanotube Models. J. Phys. Chem. C 2010, 114, 11358-11363. 46. Lecouvet, B.; Horion, J.; D’Haese, C.; Bailly, C.; Nysten, B., Elastic Modulus of Halloysite Nanotubes. Nanotech. 2013, 24, 105704-105711. 47. Song, K.; Zhang, Y.; Meng, J.; Green, E. C.; Tajaddod, N.; Li, H.; Minus, M. L., Structural Polymer-Based Carbon Nanotube Composite Fibers: Understanding the Processing–Structure–Performance Relationship. Mater. 2013, 6, 2543-2577. 48. Sato, H.; Ono, K.; Johnston, C. T.; Yamagishi, A., First-Principles Studies on the Elastic Constants of a 1: 1 Layered Kaolinite Mineral. Am. Mineral. 2005, 90, 18241826. 49. Lu, D.; Chen, H.; Wu, J.; Chan, C. M., Direct Measurements of the Young's Modulus of a Single Halloysite Nanotube Using a Transmission Electron Microscope with a Bending Stage. J. Nanosci. Nanotechnol. 2011, 11, 7789-7793. 50. Salvetat, J.-P.; Briggs, G. A. D.; Bonard, J.-M.; Bacsa, R. R.; Kulik, A. J.; Stöckli, T.; Burnham, N. A.; Forró, L., Elastic and Shear Moduli of Single-Walled Carbon Nanotube Ropes. Phys. Rev. Lett. 1999, 82, 944-947. 51. Satcurada, I.; Ito, T.; Nakamae, K., Elastic Moduli of the Crystal Lattices of Polymers. J. Polym. Sci., Part C: Polym. Symp. 1967, 15, 75-91. 52. Popov, V.; Van Doren, V.; Balkanski, M., Elastic Properties of Crystals of Single-Walled Carbon Nanotubes. Solid State Commun. 2000, 114, 395-399. S-14
53. Liu, T.; Kumar, S., Effect of Orientation on the Modulus of Swnt Films and Fibers. Nano Lett. 2003, 3, 647-650. 54. Cadek, M.; Coleman, J. N.; Ryan, K. P., Reinforcement of Polymers with Carbon Nanotubes:The Role of Nanotube Surface Area. Nano Lett. 2004, 4, 353-356.
S-15
